Categorical data analysis using the SAS system

635 Pages·2000·22.666 MB·English

by  Maura Ellen Stokes, Charles S Davis, Gary G Koch

Categorical
Data Analysis
Using
The SAS System
®
∑π∑∑k∑χπ2π∑π∑k∑πkπππ∑∑k∑χ∑2π∑χπ2kππ∑χ2k∑∑χ2πχππχπ∑∑2 ∑ππkχ∑2χπ∑πkχπk2∑χπχ2∑ π 2nd Edition
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π π ∑k χπ2∑∑k πχπ2k∑∑k πχ2π∑∑∑πχ∑2∑kππkχ∑2π∑χ2kk∑πkχ2π∑kχ2
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π ∑∑ π∑ kπ∑∑ kχ2∑k πk∑∑kχ2π∑k χk2 Maura E. Stokes
∑ π ∑ kπ π χ2 ∑
χ2πk χ2 ∑ k
k∑ ππ∑k πχ2∑kχ2π∑kχ2 χ2 Charles S. Davis
k π ∑ π
π∑ xπ2∑χ2 Gary G. Koch
∑
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The correct bibliographic citation for this manual is as follows: Stokes, Maura E., Charles S. Davis, and Gary G.
Koch. 2000. Categorical Data Analysis Using the SAS® System, Second Edition. Cary, NC: SAS Institute Inc.
Categorical Data Analysis Using the SAS® System
Copyright © 2000 by SAS Institute Inc., Cary, NC, USA
Jointly co-published by SAS Institute and Wiley 2003.
ISBN 1-58025-710-0
John Wiley & Sons, Inc. ISBN 0-471-22424-3
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SAS Institute Inc., SAS Campus Drive, Cary, North Carolina 27513.
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2nd printing, November 2001
3rd printing, June 2003
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Table of Contents
PrefacetotheSecondEdition v
Acknowledgments vii
Chapter1.Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 ScaleofMeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 SamplingFrameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 OverviewofAnalysisStrategies . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 WorkingwithTablesintheSASSystem . . . . . . . . . . . . . . . . . . . . 10
1.6 UsingThisBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter2.The2 2Table 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
(cid:2)
2.2 Chi-SquareStatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 ExactTests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Difference inProportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 OddsRatioandRelativeRisk . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.6 Sensitivity andSpecificity . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.7 McNemar’sTest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter3.Setsof2 2Tables 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
(cid:2)
3.2 Mantel-Haenszel Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Measures ofAssociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter4.Setsof2 rands 2Tables 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
(cid:2) (cid:2)
4.2 Setsof Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Setsof2 rTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
(cid:2)
4.4 Relationsship2s BetweenSetsofTables . . . . . . . . . . . . . . . . . . . . . 86
(cid:2)
Chapter5.Thes rTable 89
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
(cid:2)
5.2 Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 ExactTestsforAssociation . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Measures ofAssociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 ObserverAgreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.6 TestforOrderedDifferences . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter6.Setsofs rTables 121
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
(cid:2)
6.2 GeneralMantel-Haenszel Methodology . . . . . . . . . . . . . . . . . . . . 124
6.3 Mantel-Haenszel Applications . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 AdvancedTopic: Application toRepeatedMeasures . . . . . . . . . . . . . 137
Chapter7.NonparametricMethods 159
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.2 Wilcoxon-Mann-Whitney Test . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.3 Kruskal-Wallis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.4 Friedman’sChi-SquareTest . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.5 AlignedRanksTestforRandomizedCompleteBlocks . . . . . . . . . . . . 170
7.6 Durbin’sTestforBalancedIncomplete Blocks . . . . . . . . . . . . . . . . 171
7.7 RankAnalysisofCovariance . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Chapter8.LogisticRegression I:DichotomousResponse 181
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2 Dichotomous Explanatory Variables . . . . . . . . . . . . . . . . . . . . . . 184
8.3 UsingtheCLASSStatement . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.4 Qualitative Explanatory Variables . . . . . . . . . . . . . . . . . . . . . . . 203
8.5 Continuous andOrdinalExplanatory Variables . . . . . . . . . . . . . . . . 211
8.6 ANoteonDiagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.7 MaximumLikelihood EstimationProblemsandAlternatives . . . . . . . . . 222
8.8 ExactMethodsinLogisticRegression . . . . . . . . . . . . . . . . . . . . . 225
8.9 UsingtheCATMODandGENMODProcedures forLogisticRegression . . . 232
Appendix A:Statistical Methodology forDichotomous LogisticRegression . . . 239
Chapter9.LogisticRegression II:PolytomousResponse 241
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
9.2 OrdinalResponse: Proportional OddsModel . . . . . . . . . . . . . . . . . 243
9.3 NominalResponse: Generalized LogitsModel . . . . . . . . . . . . . . . . 257
Chapter10.ConditionalLogisticRegression 271
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
10.2 PairedObservations fromaHighlyStratifiedCohortStudy . . . . . . . . . 273
10.3 ClinicalTrialsStudyAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 276
10.4 CrossoverDesignStudies . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
10.5 GeneralConditional LogisticRegression . . . . . . . . . . . . . . . . . . . 295
10.6 PairedObservations inaRetrospective MatchedStudy . . . . . . . . . . . 300
10.7 1: Conditional LogisticRegression . . . . . . . . . . . . . . . . . . . . . 309
10.8 ExmactConditional LogisticRegression intheStratifiedSetting . . . . . . . 314
Appendix A:TheoryfortheCase-Control Retrospective Setting . . . . . . . . . 318
Appendix B:TheoryforExactConditional Inference . . . . . . . . . . . . . . . 320
Appendix C:ODSMacro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Chapter11.QuantalBioassayAnalysis 323
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
11.2 EstimatingToleranceDistributions . . . . . . . . . . . . . . . . . . . . . . 325
11.3 ComparingTwoDrugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
11.4 AnalysisofPainStudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
ii
Chapter12.PoissonRegression 347
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
12.2 Methodology forPoissonRegression . . . . . . . . . . . . . . . . . . . . . 349
12.3 SimplePoissonCountsExample . . . . . . . . . . . . . . . . . . . . . . . 351
12.4 PoissonRegressionforIncidence Densities . . . . . . . . . . . . . . . . . 353
12.5 Overdispersion inLowerRespiratory Infection Example . . . . . . . . . . 356
Chapter13.WeightedLeastSquares 363
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
13.2 WeightedLeastSquaresMethodology . . . . . . . . . . . . . . . . . . . . 365
13.3 UsingPROCCATMODforWeightedLeastSquaresAnalysis . . . . . . . . 371
13.4 AnalysisofMeans: PerformingContrastTests . . . . . . . . . . . . . . . . 377
13.5 AnalysisofProportions: Occupational Data . . . . . . . . . . . . . . . . . 386
13.6 Obstetrical PainData: AdvancedModelingofMeans . . . . . . . . . . . . 395
13.7 AnalysisofSurveySampleData . . . . . . . . . . . . . . . . . . . . . . . 409
13.8 ModelingRankMeasuresofAssociation Statistics . . . . . . . . . . . . . . 418
Appendix A:Statistical Methodology forWeightedLeastSquares . . . . . . . . 422
Chapter14.ModelingRepeatedMeasurementsDatawithWLS 427
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
14.2 WeightedLeastSquares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
14.3 AdvancedTopic: FurtherWeightedLeastSquaresApplications . . . . . . . 453
Chapter15.Generalized EstimatingEquations 469
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
15.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
15.3 SummaryoftheGEEMethodology . . . . . . . . . . . . . . . . . . . . . 478
15.4 PassiveSmokingExample . . . . . . . . . . . . . . . . . . . . . . . . . . 480
15.5 CrossoverExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
15.6 Respiratory Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
15.7 UsingaModifiedWaldStatistictoAssessModelEffects . . . . . . . . . . 503
15.8 Diagnostic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
15.9 UsingGEEforCountData . . . . . . . . . . . . . . . . . . . . . . . . . . 510
15.10 FittingtheProportional OddsModel . . . . . . . . . . . . . . . . . . . . 514
15.11 GEEAnalysesforDatawithMissingValues . . . . . . . . . . . . . . . . 518
15.12 Alternating LogisticRegression . . . . . . . . . . . . . . . . . . . . . . . 527
15.13 UsingGEEtoFitaPartialProportional OddsModel: UnivariateOutcome 533
15.14 UsingGEEtoAccountforOverdispersion: UnivariateOutcome . . . . . . 541
Appendix A:StepstoFindtheGEESolution . . . . . . . . . . . . . . . . . . . 547
Appendix B:MacroforAdjustedWaldStatistic . . . . . . . . . . . . . . . . . . 548
Chapter16.LoglinearModels 551
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
16.2 Two-WayContingency Tables . . . . . . . . . . . . . . . . . . . . . . . . 554
16.3 Three-WayContingency Tables . . . . . . . . . . . . . . . . . . . . . . . . 564
16.4 Higher-Order Contingency Tables . . . . . . . . . . . . . . . . . . . . . . 574
16.5 Correspondence BetweenLogisticModelsandLoglinear Models . . . . . . 585
iii
Appendix A:Equivalence oftheLoglinearandPoissonRegressionModels . . . 588
Chapter17.Categorized Time-to-EventData 591
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
17.2 LifeTableEstimationofSurvivalRates . . . . . . . . . . . . . . . . . . . 593
17.3 Mantel-CoxTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
17.4 PiecewiseExponential Models . . . . . . . . . . . . . . . . . . . . . . . . 599
References 607
Index 619
iv
Preface to the Second Edition
Thissecond editioncontains severalnewtopicsandincludes numerousupdatestoreflect
Version8oftheSASSystem. Chapter15,“Generalized EstimatingEquations,”isanew
chapterthatdiscusses theuseoftheGEEmethod,particularly asatoolforanalyzing
repeated measurementsdata. Thebookincludes severalcomparisons ofanalyses usingthe
GEEmethod, weightedleastsquares, andconditional logisticregression; theuseof
subject-specific modelsversuspopulation-averaged modelsisdiscussed. Chapter15also
describes theuseofGEEmethodsforsomeunivariate responsesituations.
Chapter12,“PoissonRegression,”isanewchapter onPoissonregression. Previously, this
topicwasdescribed inthechapterontime-to-event categorical data. Themethodology is
illustrated withseveralexamples.
Chaptersontheanalysis oftablesnowinclude muchmorematerialontheuseofexact
testsofassociation, particularly Chapter2,“The2 2Table,”andChapter5,“The
Table.” s r
(cid:2) (cid:2)
Exactlogisticregression usingtheLOGISTICprocedure isdiscussed inChapter8,
“LogisticRegressionI:DichotomousResponse.” Chapter8alsodescribes theuseofthe
CLASSstatementinPROCLOGISTIC,andalloftheexamplesinthevariouschapters
usingPROCLOGISTIChavebeenupdatedtotakeadvantage ofthenewCLASS
statement. Chapter10,“Conditional LogisticRegression,” hasbeenlargelyrevisedtoput
moreemphasisonthestratifieddatasetting.
Inaddition, miscellaneous revisionsandadditions appearthroughout thebook.
Computing Details
Writingabookforsoftwarethatisconstantly changing isnotstraightforward. Thissecond
editionistargeted forVersion8oftheSASSystemandtakesadvantage ofmanyofthe
featuresofthatrelease. Theexampleswereexecuted withthe8.1releaseontheHPUNIX
platform, butmostoftheoutput canbereproduced usingVersion8.0withthefollowing
changes forRelease8.1:
PROCLOGISTICaddsexactlogistic regression.
(cid:15)
PROCGENMODmodels, bydefault, theprobability ofthelowestorderedresponse
variable levels. (Thedefault hasbeenchangedfrompreviousreleases tomakeit
(cid:15)
consistent withotherprocedures.)
Tomakethingsalittlemorecomplicated, theauthorsusedanoutputtemplateforthe
LOGISTICprocedure thatwillbecomethedefaultinRelease8.2. Themaindifference is
thatthelabelforthechi-square statistic intheparameterestimatestableis“Wald
Chi-Square”inRelease8.2(whichwasthelabelusedinVersion6).
Notethat,because oflimitedspace,notalloftheoutputthatisproduced withtheexample
SAScodeisshown. Generally,theoutputpertinenttothediscussionisdisplayed. AnODS
SELECTstatementissometimesusedintheexamplecodetolimitthetablesproduced.
Forthoseusersstillrunning earlierversions oftheSASSystem,suchasRelease6.09Eon
themainframeandRelease6.12onUNIXandPCplatforms, themainadditions tothose
releaseswithVersion8aretheCLASSstatementintheLOGISTICprocedure, the
inclusion ofcompleteGEEfacilities intheGENMODprocedure, andtheavailability of
exact -valuesformanyofthetestsproduced bytheFREQprocedure. Thefirstexample
inChappter8discusseshowtouseindicatorvariables, andtheremaininglogisticregression
examplescanbeperformed withindicator variablesaswell. Release6.12doescontaina
preliminary versionoftheGEEfacilityinPROCGENMOD;refertothedocumentation
forthatreleaseformoredetail.
Someoftheprocedures suchasPROCFREQareprintingmoredigitsforvariousstatistics
andparameterestimatesthantheydidinpreviousreleases oftheSASSystem. Thiswas
donemainlytomaketheprocedures moreconsistent witheachother.
ForMore Information
TheWebsitewww.sas.com/catbook contains furtherinformation pertaining totopicsinthe
book,including archivesanderrata. Inthefuture,theseWebpageswillalsoprovide
information onusingnewfeatures inSASsoftwareforcategorical dataanalysis, aswellas
containexamplesandreferences onmethodological advances.
vi
Acknowledgments
Thesecondeditionprovedtobeasubstantialundertaking. Wearethankfulforgettingalot
ofhelpalongtheway.
WewouldliketothankOzkanZenginforhisassistance inbringingthisbookuptodatein
anumberofways,including adaptation toanewpublishing systemandrunning and
checking alloftheexamples. DanSpitznerprovidedcarefulproofing.
Numerouscolleagues contributed tothisbookwiththeirconversations, reviews,and
suggestions, andweareverygrateful fortheirtimeandeffort. WethankBobDerr,Diane
Catellier, GordonJohnston, LisaLaVange,JohnPreisser, DavidSchlotzhauer, Todd
Schwartz,andDonnaWatts.
And,ofcourse, weremainthankful tothosepersonswhohelpedtolaunchthefirstedition
withtheirsundryfeedback. TheyincludeSoniaDavis,WilliamDuckworthII,Suzanne
Edwards,StuartGansky,GregGoodwin,WendyGreene,DuaneHayes,AllisonKinkead,
AntonioPedroso-de-Lima, AnnetteSanders,CatherineTangen,LisaTomasko,andGreg
Weier.
Wealsothankourmanyreaderswhofoundthebookusefulandencouraged itscontinuing
lifeinasecond edition.
VirginiaClarkeditedthisbook.
GinnyMatseydesigned thecover.
TimArnoldprovided documentation programming support.
Chapter 1
Introduction
Chapter Table of Contents
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 ScaleofMeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 SamplingFrameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 OverviewofAnalysisStrategies . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.1 Randomization Methods . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.2 ModelingStrategies . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 WorkingwithTablesintheSASSystem . . . . . . . . . . . . . . . . . . . . 10
1.6 UsingThisBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15